To wonder is to feel curiosity or awe — I wonder whether it will rain. To wander is to move about without a fixed course. One happens in the mind, the other with the feet, and the O is the thinking one.
The core difference
Curiosity and roaming.
- wonder — feel curiosity or awe: I wonder why, a sense of wonder.
- wander — roam: wander through the market, his attention wandered.
Where they overlap
Attention wanders — it moves off course. A mind wonders — it questions. So "my mind wandered" and "my mind wondered" are both grammatical and mean different things, which is the sentence where care is needed.
The related words
Wonderful and wondrous from the first; wanderer and wanderlust from the second. Wanderlust is a direct German borrowing meaning a strong desire to travel.